Work authorization and work limits for dependents of EU Blue Card Holder

I have recently moved to Dusseldorf from the US with my spouse who is currently an EU Blue Card holder. As a dependent, I have also received a German Residence permit valid for 4 years and as far as my understanding goes, I now have a valid work authorization and can take up a job. My question is - am I eligible to take up a job only in Germany, or is my work authorization valid throughout the EU - for example, can I join company in Eindhoven, Netherlands without the need for the employer to file for a separate work authorization? I have a Masters degree from Spain, if that makes any difference. Thanks for your response in advance.